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  • Desigualdades:
  • 7x-x^2>=0 7x-x^2>=0
  • x^2+x-12<0 x^2+x-12<0
  • x^2<9 x^2<9
  • x^2-6x+9<0 x^2-6x+9<0

  • Expresiones idénticas

  • (log dos (8x))*(log cero ,1 veinticinco x(2))/(log0,5x(dieciséis))<=0,25
  • ( logaritmo de 2(8x)) multiplicar por ( logaritmo de 0,125x(2)) dividir por ( logaritmo de 0,5x(16)) menos o igual a 0,25
  • ( logaritmo de dos (8x)) multiplicar por ( logaritmo de cero ,1 veinticinco x(2)) dividir por ( logaritmo de 0,5x(dieciséis)) menos o igual a 0,25
  • (log2(8x))(log0,125x(2))/(log0,5x(16))<=0,25
  • log28xlog0,125x2/log0,5x16<=0,25
  • (log2(8x))*(log0,125x(2))/(log0,5x(16))<=O,25
  • (log2(8x))*(log0,125x(2)) dividir por (log0,5x(16))<=0,25

  • Expresiones semejantes

  • (log2(8x)*log0,125(x^2))/(log0,5x(16))<=1/4
  • ((log2(8x)*log0,125x(2))/log0,5x(16))<=1/4
Resolver desigualdades/ (log2(8x))*(log0,125x(2))/(log0,5x(16))<=0,25

(log2(8x))*(log0,125x(2))/(log0,5x(16))<=0,25 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
log(8*x)                      
--------*log(0.125*x)*2       
 log(2)                       
----------------------- <= 1/4
     log(0.5*x)*16
$$\frac{2 \log{\left(0.125 x \right)} \frac{\log{\left(8 x \right)}}{\log{\left(2 \right)}}}{16 \log{\left(0.5 x \right)}} \leq \frac{1}{4}$$ 
((2*log(0.125*x))*(log(8*x)/log(2)))/((16*log(0.5*x))) <= 1/4
Solución detallada
Se da la desigualdad:
$$\frac{2 \log{\left(0.125 x \right)} \frac{\log{\left(8 x \right)}}{\log{\left(2 \right)}}}{16 \log{\left(0.5 x \right)}} \leq \frac{1}{4}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\frac{2 \log{\left(0.125 x \right)} \frac{\log{\left(8 x \right)}}{\log{\left(2 \right)}}}{16 \log{\left(0.5 x \right)}} = \frac{1}{4}$$
Resolvemos:
$$x_{1} = 0.281571432656349$$
$$x_{2} = 14.205986602632$$
$$x_{1} = 0.281571432656349$$
$$x_{2} = 14.205986602632$$
Las raíces dadas
$$x_{1} = 0.281571432656349$$
$$x_{2} = 14.205986602632$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{1}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 0.281571432656349$$
=
$$0.181571432656349$$
lo sustituimos en la expresión
$$\frac{2 \log{\left(0.125 x \right)} \frac{\log{\left(8 x \right)}}{\log{\left(2 \right)}}}{16 \log{\left(0.5 x \right)}} \leq \frac{1}{4}$$
$$\frac{2 \log{\left(0.125 \cdot 0.181571432656349 \right)} \frac{\log{\left(0.181571432656349 \cdot 8 \right)}}{\log{\left(2 \right)}}}{16 \log{\left(0.181571432656349 \cdot 0.5 \right)}} \leq \frac{1}{4}$$
0.073631188441671       
----------------- <= 1/4
      log(2)

significa que una de las soluciones de nuestra ecuación será con:
$$x \leq 0.281571432656349$$
 _____           _____          
      \         /
-------•-------•-------
       x1      x2

Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \leq 0.281571432656349$$
$$x \geq 14.205986602632$$
Solución de la desigualdad en el gráfico
Respuesta rápida [src] 
  /   /                               _____________________________________________________________       \     /                              _____________________________________________________________         \\
  |   |                              /                                                        2           |     |                             /                                                        2             ||
  |   |          -1.95251363454387*\/  0.283560210229069 + 1.0*log(2) + 0.0655770473131347*log (2)        |     |          1.95251363454387*\/  0.283560210229069 + 1.0*log(2) + 0.0655770473131347*log (2)          ||
Or\And\x <= 2.0*e                                                                                  , 0 < x/, And\x <= 2.0*e                                                                                 , 2.0 < x//
$$\left(x \leq \frac{2.0}{e^{1.95251363454387 \sqrt{0.0655770473131347 \log{\left(2 \right)}^{2} + 0.283560210229069 + 1.0 \log{\left(2 \right)}}}} \wedge 0 < x\right) \vee \left(x \leq 2.0 e^{1.95251363454387 \sqrt{0.0655770473131347 \log{\left(2 \right)}^{2} + 0.283560210229069 + 1.0 \log{\left(2 \right)}}} \wedge 2.0 < x\right)$$ 
((0 < x)∧(x <= 2.0*exp(-1.95251363454387*sqrt(0.283560210229069 + 1.0*log(2) + 0.0655770473131347*log(2)^2))))∨((2.0 < x)∧(x <= 2.0*exp(1.95251363454387*sqrt(0.283560210229069 + 1.0*log(2) + 0.0655770473131347*log(2)^2))))
Respuesta rápida 2 [src] 
                              _____________________________________________________________                                   _____________________________________________________________ 
                             /                                                        2                                      /                                                        2     
         -1.95251363454387*\/  0.283560210229069 + 1.0*log(2) + 0.0655770473131347*log (2)                1.95251363454387*\/  0.283560210229069 + 1.0*log(2) + 0.0655770473131347*log (2)  
(0, 2.0*e                                                                                  ] U (2.0, 2.0*e                                                                                 ]
$$x\ in\ \left(0, \frac{2.0}{e^{1.95251363454387 \sqrt{0.0655770473131347 \log{\left(2 \right)}^{2} + 0.283560210229069 + 1.0 \log{\left(2 \right)}}}}\right] \cup \left(2.0, 2.0 e^{1.95251363454387 \sqrt{0.0655770473131347 \log{\left(2 \right)}^{2} + 0.283560210229069 + 1.0 \log{\left(2 \right)}}}\right]$$ 
x in Union(Interval.Lopen(0, 2.0*exp(-1.95251363454387*sqrt(0.0655770473131347*log(2)^2 + 0.283560210229069 + 1.0*log(2)))), Interval.Lopen(2.00000000000000, 2.0*exp(1.95251363454387*sqrt(0.0655770473131347*log(2)^2 + 0.283560210229069 + 1.0*log(2)))))
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